Question

What is the value of x? _____ Units​

Answer 1

Answer:

$x=25$

Step-by-step explanation:

The line QC makes:

           $\triangle DQC\sim\triangle DBR$

Using the property of similar triangles:

$\dfrac{DQ}{BD} =\dfrac{DC}{DR} \\\\\dfrac{40}{40+24} =\dfrac{x}{x+15}$

Using cross multiplication method:

$40(x+15)=x(40+24)\\\\40(x+15)=x(64)\\\\40(x)+40(15)=64x\\\\40x+600=64x$

Subtracting '$40x$' both the sides:

$64x-40x=600\\\\24x=600$

Dividing by '24' both sides:

$x=\dfrac{600}{24} \\\\x=25$

The value of 'x' in the figure is : $x=25$